CHAPTER 16
COST ALLOCATION: JOINT PRODUCTS AND BYPRODUCTS
16-1 Exhibit 16-1 presents many examples of joint products from four different general
industries. These include:
Industry
Separable Products at the Splitoff Point
Food Processing:
• Lamb
• Lamb cuts, tripe, hides, bones, fat
• Turkey
• Breasts, wings, thighs, poultry meal
Extractive:
• Petroleum
• Crude oil, natural gas
16-2 A joint cost is a cost of a production process that yields multiple products simultaneously.
A separable cost is a cost incurred beyond the splitoff point that is assignable to each of the
specific products identified at the splitoff point.
16-3 The distinction between a joint product and a byproduct is based on relative sales value.
A joint product is a product from a joint production process (a process that yields two or more
products) that has a relatively high total sales value. A byproduct is a product that has a relatively
low total sales value compared to the total sales value of the joint (or main) products. Products
can change from byproducts to joint products when their total sales values increase.
16-4 A product is any output that has a positive sales value (or an output that enables a
company to avoid incurring costs). In some joint-cost settings, outputs can occur that do not have
a positive sales value. The offshore processing of hydrocarbons yields water that is recycled back
into the ocean as well as yielding oil and gas. The processing of mineral ore to yield gold and
silver also yields dirt as an output, which is recycled back into the ground.
16-5
The chapter lists the following six reasons for allocating joint costs:
1. Computation of inventoriable costs and cost of goods sold for financial accounting
purposes and reports for income tax authorities.
2. Computation of inventoriable costs and cost of goods sold for internal reporting
purposes and division profitability analysis.
3. Cost reimbursement under contracts when only a portion of a business's products or
services is sold or delivered under cost-plus contracts.
4. Insurance settlement computations for damage claims made on the basis of cost
information of joint products or byproducts. The insurance company and the insured
must agree on the value of the loss.
5. Rate regulation when one or more of the jointly-produced products or services are
subject to price regulation.
6. Litigation in which costs of joint products are key inputs.
16-6 The joint production process yields individual products that are either sold this period or
held as inventory to be sold in subsequent periods. Hence, the joint costs need to be allocated
between total production rather than just those sold this period.
16-1
16-7 This situation can occur when a production process yields separable outputs at the splitoff
point that do not have selling prices available until further processing. The result is that selling
prices are not available at the splitoff point to use the sales value at splitoff method. Examples
include processing in integrated pulp and paper companies and in petro-chemical operations.
16-8 Both methods use market selling-price data in allocating joint costs, but they differ in which
sales-price data they use. The sales value at splitoff method allocates joint costs to joint products on
the basis of the relative total sales value at the splitoff point of the total production of these products
during the accounting period. The net realizable value method allocates joint costs to joint products
on the basis of the relative net realizable value (the final sales value minus the separable costs of
production and marketing) of the total production of the joint products during the accounting period.
16-9
Limitations of the physical measure method of joint-cost allocation include:
a. The physical weights used for allocating joint costs may have no relationship to the
revenue-producing power of the individual products.
b. The joint products may not have a common physical denominator––for example, one
may be a liquid while another a solid with no readily available conversion factor.
16-10 The NRV method can be simplified by assuming (a) a standard set of post-splitoff point
processing steps, and (b) a standard set of selling prices. The use of (a) and (b) achieves the same
benefits that the use of standard costs does in costing systems.
16-11 The constant gross-margin percentage NRV method takes account of the post-splitoff
point “profit” contribution earned on individual products, as well as joint costs, when making
cost assignments to joint products. In contrast, the sales value at splitoff point and the NRV
methods allocate only the joint costs to the individual products.
16-12 No. Any method used to allocate joint costs to individual products that is applicable to
the problem of joint product-cost allocation should not be used for management decisions
regarding whether a product should be sold or processed further. When a product is an inherent
result of a joint process, the decision to process further should not be influenced by either the
size of the total joint costs or by the portion of the joint costs assigned to particular products.
Joint costs are irrelevant for these decisions. The only relevant items for these decisions are the
incremental revenue and the incremental costs beyond the splitoff point.
16-13 No. The only relevant items are incremental revenues and incremental costs when
making decisions about selling products at the splitoff point or processing them further.
Separable costs are not always identical to incremental costs. Separable costs are costs incurred
beyond the splitoff point that are assignable to individual products. Some separable costs may
not be incremental costs in a specific setting (e.g., allocated manufacturing overhead for postsplitoff processing that includes depreciation).
16-14 Two methods to account for byproducts are:
a. Production method—recognizes byproducts in the financial statements at the time
production is completed.
b. Sales method—delays recognition of byproducts until the time of sale.
16-2
16-15 The sales byproduct method enables a manager to time the sale of byproducts to affect
reported operating income. A manager who was below the targeted operating income could
adopt a “fire-sale” approach to selling byproducts so that the reported operating income exceeds
the target. This illustrates one dysfunctional aspect of the sales method for byproducts.
16-3
16-16 (20–30 min.) Joint-cost allocation, insurance settlement.
1. (a) Sales value at splitoff method:
Breasts
Wings
Thighs
Bones
Feathers
Pounds
of
Product
100
20
40
80
10
250
Wholesale
Selling Price
per Pound
$0.55
0.20
0.35
0.10
0.05
Sales
Value
at Splitoff
$55
4
14
8
0.5
$81.5
Weighting:
Sales Value
at Splitoff
0.675
0.049
0.172
0.098
0.006
1.000
Joint
Costs
Allocated
$ 33.75
2.45
8.60
4.90
0.30
$50.00
Allocated
Costs per
Pound
0.3375
0.1225
0.2150
0.0613
0.0300
Costs of Destroyed Product
Breasts: $0.3375 per pound × 40 pounds = $13.50
Wings: $0.1225 per pound × 15 pounds =
1.84
$15.34
(b)
Physical measure method:
Breasts
Wings
Thighs
Bones
Feathers
Pounds
of
Product
100
20
40
80
10
250
Weighting:
Physical
Measures
0.400
0.080
0.160
0.320
0.040
1.000
Costs of Destroyed Product
Breast: $0.20 per pound × 40 pounds
Wings: $0.20 per pound × 15 pounds
Joint
Costs
Allocated
$ 20.00
4.00
8.00
16.00
2.00
$50.00
=
=
Allocated
Costs per
Pound
$0.200
0.200
0.200
0.200
0.200
$ 8
3
$11
Note: Although not required, it is useful to highlight the individual product profitability figures:
Product
Breasts
Wings
Thighs
Bones
Feathers
Sales
Value
$55
4
14
8
0.5
Sales Value at
Splitoff Method
Joint Costs
Gross
Allocated
Income
$33.75
$21.25
2.45
1.55
8.60
5.40
4.90
3.10
0.30
0.20
16-4
Physical
Measures Method
Joint Costs
Gross
Allocated
Income
$20.00
$35.00
4.00
0.00
8.00
6.00
16.00
(8.00)
2.00
(1.50)
2.
The sales-value at splitoff method captures the benefits-received criterion of cost
allocation and is the preferred method. The costs of processing a chicken are allocated to
products in proportion to the ability to contribute revenue. Quality Chicken’s decision to
process chicken is heavily influenced by the revenues from breasts and thighs. The bones
provide relatively few benefits to Quality Chicken despite their high physical volume.
The physical measures method shows profits on breasts and thighs and losses on
bones and feathers. Given that Quality Chicken has to jointly process all the chicken
products, it is non-intuitive to single out individual products that are being processed
simultaneously as making losses while the overall operations make a profit. Quality
Chicken is processing chicken mainly for breasts and thighs and not for wings, bones,
and feathers, while the physical measure method allocates a disproportionate amount of
costs to wings, bones and feathers.
16-5
16-17 (10 min.) Joint products and byproducts (continuation of 16-16).
1.
Ending inventory:
Breasts
12
Wings
5
Thighs
7
Bones
6
Feathers
3
×
×
×
×
×
$0.3375
0.1225
0.2150
0.0613
0.0300
= $4.0500
= 0.6125
= 1.5050
= 0.3678
= 0.0900
$6.6253
2.
Joint products
Breasts
Thighs
Byproducts
Wings
Bones
Feathers
Net Realizable Values of byproducts:
Wings
$ 4
Bones
8
Feathers
0.5
$12.5
Joint costs to be allocated:
Joint costs – Net Realizable Values of byproducts
$50 – $12.5 = $37.5
Breast
Thighs
Pounds
of
Product
Wholesale
Selling Price
per Pound
Sales
Value
at Splitoff
Weighting:
Sales Value
at Splitoff
Joint
Costs
Allocated
Allocated
Costs Per
Pound
100
40
$0.55
0.35
$55
14
$69
55/69
14/69
$29.89
7.61
$37.50
$0.2989
0.1903
Ending inventory:
Breasts 12 × $0.2989
Thighs 7 × 0.1903
3.
$3.5868
1.3321
$4.9189
Treating all products as joint products does not require judgments as to whether a product
is a joint product or a byproduct. Joint costs are allocated in a consistent manner to all
products for the purpose of costing and inventory valuation. In contrast, the approach in
requirement 2 lowers the joint cost by the amount of byproduct net realizable values and
results in inventory values being shown for only two of the five products, the ones
(perhaps arbitrarily) designated as being joint products.
16-6
16-18 (10 min.) Net realizable value method.
A diagram of the situation is in Solution Exhibit 16-18.
Final sales value of total production,
12,500 × $50; 6,250 × $25
Deduct separable costs
Net realizable value at splitoff point
Weighting, $250,000; $62,500 ÷ $312,500
Joint costs allocated, 0.8; 0.2 × $325,000
Corn Syrup
Corn Starch
$625,000
375,000
$250,000
0.8
$260,000
$156,250
93,750
$ 62,500
0.2
$ 65,000
Total
$781,250
468,750
$312,500
$325,000
SOLUTION EXHIBIT 16-18 (all numbers are in thousands)
Joint Costs
Separable Costs
Processing
$375,000
Corn Syrup:
12,500 cases at
$50 per case
Processing
$93,750
Corn Starch:
6,250 cases at
$25 per case
Processing
$325,000
Splitoff
Point
16-7
16-19 (40 min.) Alternative joint-cost-allocation methods, further-process decision.
A diagram of the situation is in Solution Exhibit 16-19.
1.
Methanol
Physical measure of total production (gallons)
3,000
Weighting, 3,000; 9,000 ÷ 12,000
0.25
Joint costs allocated, 0.25; 0.75 × $150,000
$ 37,500
2.
3.
Turpentine
Total
9,000
0.75
$ 112,500
12,000
Methanol
Turpentine
$150,000
Total
Final sales value of total production,
3,000 × $22.00; 9,000 × $15.00
Deduct separable costs,
3,000 × $4.00; 9,000 × $3.00
Net realizable value at splitoff point
$ 66,000
$135,000
$201,000
12,000
$ 54,000
27,000
$ 108,000
39,000
$162,000
Weighting, $54,000; $108,000 ÷ $162,000
Joint costs allocated, 1/3; 2/3 × $150,000
1/3
$ 50,000
2/3
$100,000
$150,000
Methanol
$66,000
Turpentine
$135,000
Total
$201,000
37,500
12,000
49,500
$16,500
112,500
27,000
139,500
$ (4,500)
150,000
39,000
189,000
$ 12,000
Methanol
$66,000
Turpentine
$135,000
Total
$201,000
50,000
12,000
62,000
$ 4,000
100,000
27,000
127,000
$ 8,000
150,000
39,000
189,000
$ 12,000
a.
Physical-measure (gallons) method:
Revenues
Cost of goods sold:
Joint costs
Separable costs
Total cost of goods sold
Gross margin
b.
Estimated net realizable value method:
Revenues
Cost of goods sold:
Joint costs
Separable costs
Total cost of goods sold
Gross margin
16-8
4.
Alcohol Bev.
Final sales value of total production,
3,000 × $65.00; 9,000 × $15.00
$195,000
Deduct separable costs,
(3,000 × $14.00) + (0.20 × $195,000);
9,000 × $3.00
81,000
Net realizable value at splitoff point
$ 114,000
Weighting, $114,000; $108,000 ÷ $222,000
0.51
Joint costs allocated, 0.51; 0.49 × $150,000
$ 76,500
Turpentine
$135,000
$330,000
27,000
$ 108,000
0.49
$ 73,500
108,000
$222,000
An incremental approach demonstrates that the company should use the new process:
Incremental revenue,
($65.00 – $22.00) × 3,000
Incremental costs:
Added processing, $10.00 × 3,000
Taxes, (0.20 × $65.00) × 3,000
Incremental operating income from
further processing
Proof:
Total sales of both products
Joint costs
Separable costs
Cost of goods sold
New gross margin
Old gross margin
Difference in gross margin
16-9
$ 129,000
$30,000
39,000
Total
(69,000)
$ 60,000
$330,000
150,000
108,000
258,000
72,000
12,000
$ 60,000
$150,000
SOLUTION EXHIBIT 16-19
Joint Costs
Separable Costs
3,000
gallons
Processing
$4 per gallon
Methanol:
3,000 gallons
at $22 per gallon
9,000
gallons
Processing
$3 per gallon
Turpentine:
9,000 gallons
at $15 per gallon
Processing
$150,000
for 12,000
gallons
Splitoff
Point
16-10
16-20 (40 min.) Alternative methods of joint-cost allocation, ending inventories.
Total production for the year was:
X
Y
Z
Sold
120
340
475
Ending
Inventories
180
60
25
Total
Production
300
400
500
A diagram of the situation is in Solution Exhibit 16-20.
1.
a.
Net realizable value (NRV) method:
X
Final sales value of total production,
300 × $1,500; 400 × $1,000; 500 × $700
Deduct separable costs
Net realizable value at splitoff point
Weighting, $450; $400; $150 ÷ $1,000
Joint costs allocated,
0.45, 0.40, 0.15 × $400,000
Y
Z
Total
$450,000
––
$450,000
$400,000
––
$400,000
$350,000
200,000
$150,000
$1,200,000
200,000
$1,000,000
0.45
0.40
0.15
$180,000
$160,000
$ 60,000
X
180
300
60%
Y
60
400
15%
$ 400,000
Ending Inventory Percentages:
Ending inventory
Total production
Ending inventory percentage
Z
25
500
5%
Income Statement
X
Revenues,
120 × $1,500; 340 × $1,000; 475 × $700
Cost of goods sold:
Joint costs allocated
Separable costs
Production costs
Deduct ending inventory,
60%; 15%; 5% of production costs
Cost of goods sold
Gross margin
Gross-margin percentage
Y
Z
Total
$180,000
$340,000
$332,500
$852,500
180,000
––
180,000
160,000
––
160,000
60,000
200,000
260,000
400,000
200,000
600,000
108,000
72,000
$108,000
24,000
136,000
$204,000
13,000
247,000
$ 85,500
145,000
455,000
$397,500
60%
60%
25.71%
16-11
b.
Constant gross-margin percentage NRV method:
Step 1:
Final sales value of prodn., (300 × $1,500) + (400 × $1,000) + (500 × $700)
Deduct joint and separable costs, $400,000 + $200,000
Gross margin
Gross-margin percentage, $600,000 ÷ $1,200,000
$1,200,000
600,000
$ 600,000
50%
Step 2:
X
Final sales value of total production,
300 × $1,500; 400 × $1,000; 500 × $700
Deduct gross margin, using overall
gross-margin percentage of sales, 50%
Total production costs
Step 3: Deduct separable costs
Joint costs allocated
Y
Z
Total
$450,000
$400,000
$350,000
$1,200,000
225,000
225,000
200,000
200,000
175,000
175,000
600,000
600,000
—
$225,000
—
$200,000
200,000
200,000
$(25,000) $ 400,000
The negative joint-cost allocation to Product Z illustrates one “unusual” feature of the
constant gross-margin percentage NRV method: some products may receive negative cost
allocations so that all individual products have the same gross-margin percentage.
Income Statement
Revenues, 120 × $1,500;
340 × $1,000; 475 × $700
Cost of goods sold:
Joint costs allocated
Separable costs
Production costs
Deduct ending inventory,
60%; 15%; 5% of production costs
Cost of goods sold
Gross margin
Gross-margin percentage
X
Y
Z
Total
$180,000
$340,000
$332,500
$852,500
225,000
225,000
200,000
200,000
(25,000)
200,000
175,000
400,000
200,000
600,000
135,000
90,000
$ 90,000
50%
30,000
170,000
$170,000
50%
8,750
166,250
$166,250
50%
173,750
426,250
$426,250
50%
16-12
Summary
a.
NRV method:
Inventories on balance sheet
Cost of goods sold on income statement
b.
Y
Z
Total
$108,000
72,000
$ 24,000
136,000
$ 13,000
247,000
$145,000
455,000
$600,000
$135,000
90,000
$ 30,000
170,000
$ 8,750
166,250
$173,750
426,250
$600,000
Constant gross-margin
percentage NRV method
Inventories on balance sheet
Cost of goods sold on income statement
2.
X
Gross-margin percentages:
X
60%
50%
NRV method
Constant gross-margin percentage NRV
Y
60%
50%
Z
25.71%
50.00%
SOLUTION EXHIBIT 16-20
Joint Costs
Separable Costs
Product X:
300 tons at
$1,500 per ton
Joint
Processing
Costs
$400,000
Product Y:
400 tons at
$1,000 per ton
Processing
$200,000
Splitoff
Point
16-13
Product Z:
500 tons at
$700 per ton
16-21 (30 min.) Joint-cost allocation, process further.
Joint Costs =
$2,100
ICR8
(Non-Saleable)
Processing
$170
Crude Oil
200 bbls × $15 / bbl =
$3,000
ING4
(Non-Saleable)
Processing
$100
NGL
100 bbls × $7 / bbl =
$700
XGE3
(Non-Saleable)
Processing
$200
Gas
700 eqvt bbls ×
$1.10 / eqvt bbl =
$770
Splitoff
Point
1a.
Physical Measure Method
1. Physical measure of total prodn.
2. Weighting (200; 100; 700 ÷ 1,000)
3. Joint costs allocated (Weights × $2,100)
1b.
1.
2.
3.
4.
5.
Crude Oil
200
0.20
$420
NGL
100
0.10
$210
Crude Oil
$3,000
170
$2,830
0.7075
$1,485.75
NGL
$700
100
$600
0.1500
$315.00
Gas
700
0.70
$1,470
Total
1,000
1.00
$2,100
NRV Method
Final sales value of total production
Deduct separable costs
NRV at splitoff
Weighting (2,830; 600; 570 ÷ 4,000)
Joint costs allocated (Weights × $2,100)
16-14
Gas
$770
200
$ 570
0.1425
$299.25
Total
$4,470
470
$4,000
$2,100
2.
The operating-income amounts for each product using each method is:
(a)
Physical Measure Method
Revenues
Cost of goods sold
Joint costs
Separable costs
Total cost of goods sold
Gross margin
(b)
Crude Oil
$3,000
NGL
$700
Gas
$770
Total
$4,470
420
170
590
$2,410
210
100
310
$390
1,470
200
1,670
$ (900)
2,100
470
2,570
$1,900
Crude Oil
$3,000.00
NGL
$700.00
Gas
$770.00
Total
$4,470.00
1,485.75
170.00
1,655.75
$1,344.25
315.00
100.00
415.00
$285.00
299.25
200.00
499.25
$ 270.75
2,100.00
470.00
2,570.00
$1,900.00
NRV Method
Revenues
Cost of goods sold
Joint costs
Separable costs
Total cost of goods sold
Gross margin
3.
Neither method should be used for product emphasis decisions. It is inappropriate to use
joint-cost-allocated data to make decisions regarding dropping individual products, or
pushing individual products, as they are joint by definition. Product-emphasis decisions
should be made based on relevant revenues and relevant costs. Each method can lead to
product emphasis decisions that do not lead to maximization of operating income.
4.
Since crude oil is the only product subject to taxation, it is clearly in Plumpton’s best
interest to use the NRV method since it leads to a lower profit for crude oil and,
consequently, a smaller tax burden. A letter to the taxation authorities could stress the
conceptual superiority of the NRV method. Chapter 16 argues that, using a benefitsreceived cost allocation criterion, market-based joint cost allocation methods are
preferable to physical-measure methods. A meaningful common denominator (revenues)
is available when the sales value at splitoff point method or NRV method is used. The
physical-measures method requires nonhomogeneous products (liquids and gases) to be
converted to a common denominator.
16-15
16-22 (30 min.) Joint-cost allocation, sales value, physical measure, NRV methods.
1a.
PANEL A: Allocation of Joint Costs using Sales Value at
Splitoff Method
Sales value of total production at splitoff point
(10,000 tons × $10 per ton; 20,000 × $15 per ton)
Weighting ($100,000; $300,000 ÷ $400,000)
Joint costs allocated (0.25; 0.75 × $240,000)
PANEL B: Product-Line Income Statement for June 2009
Revenues
(12,000 tons × $18 per ton; 24,000 × $25 per ton)
Deduct joint costs allocated (from Panel A)
Deduct separable costs
Gross margin
Gross margin percentage
Special B/
Beef
Ramen
Special S/
Shrimp
Ramen
$100,000
0.25
$60,000
$300,000
0.75
$180,000
Special B
Special S
$216,000
60,000
48,000
$108,000
50%
$600,000
180,000
168,000
$252,000
42%
$816,000
240,000
216,000
$360,000
44%
Special B/
Beef
Ramen
10,000
33%
$80,000
Special S/
Shrimp
Ramen
20,000
67%
$160,000
Total
30,000
$240,000
Special B
Special S
Total
Total
$400,000
$240,000
Total
1b.
PANEL A: Allocation of Joint Costs using Physical-Measure
Method
Physical measure of total production (tons)
Weighting (10,000 tons; 20,000 tons ÷ 30,000 tons)
Joint costs allocated (0.33; 0.67 × $240,000)
PANEL B: Product-Line Income Statement for June 2009
Revenues
(12,000 tons × $18 per ton; 24,000 × $25 per ton)
Deduct joint costs allocated (from Panel A)
Deduct separable costs
Gross margin
Gross margin percentage
$216,000
80,000
48,000
$ 88,000
41%
$600,000
160,000
168,000
$272,000
45%
$816,000
240,000
216,000
$360,000
44%
1c.
PANEL A: Allocation of Joint Costs using Net Realizable
Value Method
Final sales value of total production during accounting period
(12,000 tons × $18 per ton; 24,000 tons × $25 per ton)
Deduct separable costs
Net realizable value at splitoff point
Weighting ($168,000; $432,000 ÷ $600,000)
Joint costs allocated (0.28; 0.72 × $240,000)
PANEL B: Product-Line Income Statement for June 2009
Revenues (12,000 tons × $18 per ton; 24,000 tons × $25 per ton)
Deduct joint costs allocated (from Panel A)
Deduct separable costs
Gross margin
Gross margin percentage
16-16
Special B
Special S
Total
$216,000
48,000
$168,000
28%
$67,200
$600,000
168,000
$432,000
72%
$172,800
$816,000
216,000
$600,000
Special B
$216,000
67,200
48,000
$100,800
46.7%
Special S
$600,000
172,800
168,000
$ 259,200
43.2%
Total
$816,000
240,000
216,000
$ 360,000
44.1%
$240,000
2.
Sherrie Dong probably performed the analysis shown below to arrive at the net loss of
$2,228 from marketing the stock:
PANEL A: Allocation of Joint Costs using
Sales Value at Splitoff
Sales value of total production at splitoff point
(10,000 tons × $10 per ton; 20,000 × $15 per
ton; 4,000 × $5 per ton)
Weighting
($100,000; $300,000; $20,000 ÷ $420,000)
Joint costs allocated
(0.238095; 0.714286; 0.047619 × $240,000)
PANEL B: Product-Line Income Statement
for June 2009
Revenues
(12,000 tons × $18 per ton; 24,000 × $25 per ton;
4,000 × $5 per ton)
Separable processing costs
Joint costs allocated (from Panel A)
Gross margin
Deduct marketing costs
Operating income
Special B/
Beef
Ramen
Special S/
Shrimp
Ramen
Stock
$100,000
$300,000
$20,000
$420,000
23.8095%
71.4286%
4.7619%
100%
$57,143
$171,429
$11,428
$240,000
Special S
Stock
Total
$600,000
168,000
171,429
260,571
$20,000
0
11,428
8,572
10,800
($2,228)
$836,000
216,000
240,000
380,000
10,800
$ 369,200
Special B
$216,000
48,000
57,143
110,857
Total
In this (misleading) analysis, the $240,000 of joint costs are re-allocated between Special B,
Special S, and the stock. Irrespective of the method of allocation, this analysis is wrong. Joint
costs are always irrelevant in a process-further decision. Only incremental costs and revenues
past the splitoff point are relevant. In this case, the correct analysis is much simpler: the
incremental revenues from selling the stock are $20,000, and the incremental costs are the
marketing costs of $10,800. So, Instant Foods should sell the stock—this will increase its
operating income by $9,200 ($20,000 – $10,800).
16-17
16-23 (20 min.) Joint cost allocation: sell immediately or process further.
1.
a.
Sales value at splitoff method:
Sales value of total production at splitoff,
600lbs × $1.20; 120 gallons × $4.80
Weighting, $720; $576 ÷ $1,296
Joint costs allocated,
0.556; 0.444 × $600
b.
Cookies/
Soymeal
$720
Soyola/
Soy Oil
$576
0.556
0.444
Total
$1,296
$334
$266
$600
Cookies
Soyola
Total
$1,728
360
$1,368
0.74
$720
240
$480
0.26
$2,448
600
$1,848
$444
$156
$600
Net realizable value method:
Final sales value of total production,
720lbs × $2.40; 480qts × $1.50
Deduct separable costs
Net realizable value
Weighting, $1,368; $480 ÷ $1,848
Joint costs allocated,
0.74; 0.26 × $600
2.
Sell at Splitoff – Revenue
Process Further - NRV
Profit (Loss) from Processing Further
Cookies/Soy Meal
$720a
$1,368 c
$648
Soyola/Soy Oil
$576 b
$480 d
($96)
a
600 lbs × $1.20 = $720
120 gal × $4.80 = $576
c
720 lbs × $2.40 – $360 = $1,368
d
480 qts × $1.50 – $240 = $480
b
ISP should process the soy meal into cookies because it increases profit by $648
(1,368-720). However, they should sell the soy oil as is, without processing it into the
form of Soyola, because profit will be $96 (576-480) higher if they do. Since the total
joint cost is the same under both allocation methods, it is not a relevant cost to the
decision to sell at splitoff or process further.
16-18
16-24 (30 min.) Accounting for a main product and a byproduct.
Production
Method
1.
Revenues
Main product
Byproduct
Total revenues
Cost of goods sold
Total manufacturing costs
Deduct value of byproduct production
Net manufacturing costs
Deduct main product inventory
Cost of goods sold
Gross margin
32,000 × $20.00
8,000 × $5.00
c
(8,000/40,000) × $440,000 = $88,000
a
b
2.
a
Main Product
Byproduct
d
e
Sales
Method
$640,000a
—
640,000
$640,000
28,000d
668,000
480,000
40,000b
440,000
88,000c
352,000
$ 288,000
480,000
0
480,000
96,000e
384,000
$ 284,000
5,600 × $5.00
(8,000/40,000) × $480,000 = $96,000
Production
Method
$88,000
12,000a
Sales
Method
$96,000
0
Ending inventory shown at unrealized selling price.
BI + Production – Sales = EI
0 + 8,000 – 5,600 = 2,400 pounds
Ending inventory = 2,400 pounds × $5 per pound = $12,000
16-19
16-25 (35–45 min.) Joint costs and byproducts.
1.
Computing byproduct deduction to joint costs:
Revenues from C, 40,000 × $3
Deduct:
Gross margin, 10% of revenues
Marketing costs, 25% of revenues
Peanut Butter Department separable costs
Net realizable value (less gross margin) of C
$120,000
Joint costs
Deduct byproduct contribution
Net joint costs to be allocated
$320,000
58,000
$262,000
16-20
12,000
30,000
20,000
$58,000
Quantity
A
20,000
B
120,000
Totals
A
B
Totals
Deduct
Net
Unit
Final
Separable
Sales
Sales
Processing
Price
Value
Cost
$10 $ 200,000
$40,000
2
240,000
––
$440,000
$40,000
Joint Costs
Allocation
$104,800
157,200
$262,000
Add Separable
Processing
Costs
$40,000
––
$40,000
Realizable
Value at
Splitoff
$ 160,000
240,000
$400,000
Total Costs
$144,800
157,200
$302,000
Weighting
40%
60%
Units
20,000
120,000
140,000
Allocation of
$262,000
Joint Costs
$104,800
157,200
$262,000
Unit Cost
$7.24
1.31
Unit cost for C: $1.45 ($58,000 ÷ 40,000) + $0.50 ($20,000 ÷ 40,000) = $1.95,
or
$3.00 – $0.30 (10% × $3) – $0.75 (25% × $3) = $1.95.
2.
If all three products are treated as joint products:
Quantity
A
20,000
B
120,000
C
40,000
Totals
A
B
C
Totals
Unit
Final
Sales
Sales
Price
Value
$10
$ 200,000
2
240,000
3
120,000
$560,000
Joint Costs
Allocation
$108,936
163,404
47,660
$320,000
Deduct
Separable
Processing
Cost
$40,000
50,000
$90,000
Add Separable
Processing
Costs
$40,000
––
20,000
$60,000
Net
Realizable
Value at
Splitoff
$ 160,000
240,000
70,000
$470,000
Total Costs
$148,936
163,404
67,660
$380,000
Weighting
160/470
240/470
70/470
Units
20,000
120,000
40,000
180,000
Allocation of
$320,000
Joint Costs
$108,936
163,404
47,660
$320,000
Unit Cost
$7.45
1.36
1.69
Call the attention of students to the different unit “costs” resulting from the two assumptions
about the relative importance of Product C. The point is that costs of individual products depend
heavily on which assumptions are made and which accounting methods and techniques are used.
16-21
16-26 (25 min.) Accounting for a byproduct.
1.
Byproduct recognized at time of production:
Joint Cost = $1,500
Joint cost to be charged to main product = Joint Cost – NRV of Byproduct
= $1,500 – (50 lbs. × $1.20)
= $1,440
$1440
Inventoriable cost of main product = 400 containers = $3.60 per container
Inventoriable cost of byproduct = NRV = $1.20 per pound
Gross Margin Calculation under Production Method
Revenues
Main product: Water (600/2 containers × $8)
Byproduct: Sea Salt
Cost of goods sold
Main product: Water (300 containers × $3.60)
$2,400
0
$2,400
_____
$1,080
Gross margin
Gross-margin percentage ($1,320 ÷ $2,400)
$1,320
55.00%
Inventoriable costs (end of period):
Main product: Water (100 containers × $3.60) = $360
Byproduct: Sea Salt (10 pounds × $1.20) = $12
2.
Byproduct recognized at time of sale:
Joint cost to be charged to main product = Total Joint Cost = $1,500
$1500
Inventoriable cost of main product = 400 containers = $3.75 per container
Inventoriable cost of byproduct = $0
16-22
Gross Margin Calculation under Sales Method
Revenues
Main product: Water (600/2 containers × $8)
Byproduct: Sea Salt (40 pounds × $1.20)
Cost of goods sold
Main product: Water (300 containers × $3.75)
$2,400
48
$2,448
_____
$1,125
Gross margin
Gross-margin percentage ($1,323 ÷ $2,448)
$1,323
54.04%
Inventoriable costs (end of period):
Main product: Water (100 containers × $3.75) = $375
Byproduct: Sea Salt (10 pounds × $0) = $0
3.
The production method recognizes the byproduct cost as inventory in the period it is
produced. This method sets the cost of the byproduct inventory equal to its net realizable
value. When the byproduct is sold, inventory is reduced without being expensed through
the income statement. The sales method associates all of the production cost with the
main product. Under this method, the byproduct has no inventoriable cost and is
recognized only when it is sold.
16-23
16-27 (40 min.) Alternative methods of joint-cost allocation, product-mix decisions.
A diagram of the situation is in Solution Exhibit 16-27.
1.
a.
Computation of joint-cost allocation proportions:
Sales Value of
Total Production
at Splitoff
A
$ 62,500
B
37,500
C
62,500
D
87,500
$250,000
Weighting
625/2500 = 0.25
375/2500 = 0.15
625/2500 = 0.25
875/2500 = 0.35
1.00
Allocation of $125,000
Joint Costs
$ 31,250
18,750
31,250
43,750
$125,000
Weighting
3750/6250 = 0.60
1250/6250 = 0.20
625/6250 = 0.10
625/6250 = 0.10
1.00
Allocation of $125,000
Joint Costs
$ 75,000
25,000
12,500
12,500
$125,000
b.
A
B
C
D
Physical Measure
of Total Production
375,000 gallons
125,000 gallons
62,500 gallons
62,500 gallons
625,000 gallons
c.
Final Sales
Value of
Total
Separable
Production
Costs
Super A $375,000
$250,000
Super B 125,000
100,000
C
52,500
–
Super D 150,000
112,500
Net
Realizable
Value at
Splitoff
$125,000
25,000
62,500
37,500
$250,000
16-24
Weighting
1250/2500 = 0.50
250/2500 = 0.10
625/2500 = 0.25
375/2500 = 0.15
1.00
Allocation of
$125,000
Joint Costs
$ 62,500
12,500
31,250
18,750
$125,000
Computation of gross-margin percentages:
a.
Sales value at splitoff method:
Super A Super B
$375,000 $125,000
31,250
18,750
250,000
100,000
281,250
118,750
$ 93,750 $ 6,250
25%
5%
Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
Gross-margin percentage
b.
Super D
$150,000
43,750
112,500
156,250
$ (6,250)
(4.17%)
Total
$712,500
125,000
462,500
587,500
$125,000
17.54%
Physical-measure method:
Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
Gross-margin percentage
c.
C
$62,500
31,250
0
31,250
$31,250
50%
Super A Super B
$375,000 $125,000
75,000
25,000
250,000
100,000
325,000
125,000
$ 50,000 $
0
0%
13.33%
C
$62,500
12,500
0
12,500
$50,000
80%
Super D
$150,000
12,500
112,500
125,000
$ 25,000
16.67%
Total
$712,500
125,000
462,500
587,500
$125,000
17.54%
Net realizable value method:
Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
Gross-margin percentage
Super A
$375,000
62,500
250,000
312,500
$ 62,500
Super B
$125,000
12,500
100,000
112,500
$ 12,500
C
$62,500
31,250
0
31,250
$31,250
Super D
Total
$150,000 $712,500
18,750 125,000
112,500 462,500
131,250 587,500
$ 18,750 $125,000
16.67%
10%
50%
12.5%
Super B
C
Super D
Summary of gross-margin percentages:
Joint-Cost
Allocation Method
Super A
Sales value at splitoff
25.00%
5%
50%
(4.17)%
Physical measure
13.33%
0%
80%
16.67%
Net realizable value
16.67%
10%
50%
12.50%
16-25
17.54%
2.
Further Processing of A into Super A:
Incremental revenue, $375,000 – $62,500
Incremental costs
Incremental operating income from further processing
$312,500
250,000
$ 62,500
Further processing of B into Super B:
Incremental revenue, $125,000 – $37,500
Incremental costs
Incremental operating loss from further processing
$ 87,500
100,000
$ (12,500)
Further Processing of D into Super D:
Incremental revenue, $150,000 – $87,500
Incremental costs
Incremental operating loss from further processing
$ 62,500
112,500
$ (50,000)
Operating income can be increased by $62,500 if both B and D are sold at their splitoff point
rather than processed further into Super B and Super D.
SOLUTION EXHIBIT 16-27
Revenues at Splitoff
and Separable Costs
Joint Costs
A, 375,000 gallons
Revenue = $62,500
B, 125,000 gallons
Revenue = $37,500
Processing
$125,000
Processing
$250,000
Super A
$375,000
Processing
$100,000
Super B
$125,000
Processing
$112,500
Super D
$150,000
C, 62,500 gallons
Revenue = $62,500
D, 62,500 gallons
Revenue = $87,500
Splitoff
Point
16-26
16-28 (40–60 min.) Comparison of alternative joint-cost allocation methods, furtherprocessing decision, chocolate products.
Joint Costs
$30,000
Separable Costs
ChocolatePowder Liquor
Base
Cocoa
Beans
Processing
$12,750
Chocolate
Powder
Processing
Milk-Chocolate
Liquor Base
Processing
$26,250
Milk
Chocolate
SPLITOFF
POINT
1a.
Sales value at splitoff method:
Sales value of total production at splitoff,
600 × $21; 900 × $26
Weighting, $12,600; $23,400 ÷ $36,000
Joint costs allocated,
0.35; 0.65 × $30,000
ChocolatePowder/
Liquor Base
MilkChocolate/
Liquor Base
$12,600
0.35
$23,400
0.65
$36,000
$10,500
$19,500
$30,000
600 gallons
900 gallons
1,500
gallons
0.40
0.60
$12,000
$18,000
Total
1b.
Physical-measure method:
Physical measure of total production
(15,000 ÷ 1,500) × 60; 90
Weighting, 600; 900 ÷ 1,500
Joint costs allocated,
0.40; 0.60 × $30,000
16-27
$30,000
1c.
Net realizable value method:
Final sales value of total production,
6,000 × $4; 10,200 × $5
Deduct separable costs
Net realizable value at splitoff point
Weighting, $11,250; $24,750 ÷ $36,000
Joint costs allocated,
0.3125; 0.6875 × $30,000
d.
ChocolatePowder
MilkChocolate
$24,000
12,750
$11,250
0.3125
$51,000
26,250
$ 24,750
0.6875
$75,000
39,000
$36,000
$9,375
$20,625
$30,000
Total
Constant gross-margin percentage NRV method:
Step 1:
Final sales value of total production, (6,000 × $4) + (10,200 × $5)
Deduct joint and separable costs, ($30,000 + $12,750 + $26,250)
Gross margin
Gross-margin percentage ($6,000 ÷ $75,000)
$75,000
69,000
$ 6,000
8%
Step 2:
Final sales value of total production,
6,000 × $4; 10,200 × $5
Deduct gross margin, using overall
gross-margin percentage of sales (8%)
Total production costs
ChocolatePowder
MilkChocolate
Total
$24,000
$51,000
$75,000
1,920
22,080
4,080
46,920
6,000
69,000
12,750
$9,330
26,250
$ 20,670
39,000
$30,000
Step 3:
Deduct separable costs
Joint costs allocated
16-28
2.
a.
b.
c.
Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
ChocolatePowder
$24,000
10,500
12,750
23,250
$ 750
MilkChocolate
$51,000
19,500
26,250
45,750
$ 5,250
Total
$75,000
30,000
39,000
69,000
$ 6,000
Gross-margin percentage
3.125%
10.294%
8%
Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
$24,000
12,000
12,750
24,750
$ (750)
$51,000
18,000
26,250
44,250
$ 6,750
$75,000
30,000
39,000
69,000
$ 6,000
Gross-margin percentage
(3.125)%
13.235%
8%
Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
$24,000
9,375
12,750
22,125
$ 1,875
$51,000
20,625
26,250
46,875
$ 4,125
$75,000
30,000
39,000
69,000
$ 6,000
Gross-margin percentage
d.
7.812%
Revenues
Joint costs
Separable costs
Total cost of goods sold
Gross margin
$24,000
9,330
12,750
22,080
$ 1,920
Gross-margin percentage
8%
16-29
8.088%
8%
$51,000
20,670
26,250
46,920
$ 4,080
$75,000
30,000
39,000
69,000
$ 6,000
8%
8%
3.
Further processing of chocolate-powder liquor base into chocolate powder:
Incremental revenue, $24,000 – $12,600
Incremental costs
Incremental operating income from further processing
$ 11,400
12,750
$ (1,350)
Further processing of milk-chocolate liquor base into milk chocolate:
Incremental revenue, $51,000 – $23,400
Incremental costs
Incremental operating income from further processing
$ 27,600
26,250
$ 1,350
Chocolate Factory could increase operating income by $1,350 (to $7,350) if chocolate-powder
liquor base is sold at the splitoff point and if milk-chocolate liquor base is further processed into
milk chocolate.
16-30
16-29 (30 min.) Joint-cost allocation, process further or sell.
A diagram of the situation is in Solution Exhibit 16-29.
1.
a. Sales value at splitoff method.
Monthly
Unit
Output
Studs
(Building)
Decorative
Pieces
Posts
Totals
Selling
Price
Per Unit
Sales Value
of Total
Prodn.
at Splitoff
90,000
$ 8
$ 720,000
46.1539%
$ 553,847
6,000
24,000
60
20
360,000
480,000
$1,560,000
23.0769
30.7692
100.0000%
276,923
369,230
$1,200,000
Physical
Measure of
Total Prodn.
90,000
6,000
24,000
120,000
Weighting
75.00%
5.00
20.00
100.00%
Joint Costs
Allocated
$ 900,000
60,000
240,000
$1,200,000
Net
Realizable
Value at
Splitoff
Weighting
Joint Costs
Allocated
Weighting
Joint Costs
Allocated
b. Physical measure at splitoff method.
Studs (Building)
Decorative Pieces
Posts
Totals
c. Net realizable value method.
Monthly
Units of
Total
Prodn.
Studs
(Building)
Decorative
Pieces
Posts
Totals
a
b
90,000
5,400
24,000
a
Fully
Processed
Selling
Price
per Unit
$ 8
$ 720,000
100
20
430,000
480,000
$1,630,000
b
6,000 monthly units of output – 10% normal spoilage = 5,400 good units.
5,400 good units × $100 = $540,000 – Further processing costs of $110,000 = $430,000
16-31
44.1718%
$ 530,061
26.3804
29.4478
100.0000%
316,565
353,374
$1,200,000
2.
Presented below is an analysis for Sundown Sawmill, Inc., comparing the processing of
decorative pieces further versus selling the rough-cut product immediately at splitoff:
Monthly unit output
Less: Normal further processing shrinkage
Units available for sale
Final sales value (5,400 units × $100 per unit)
Less: Sales value at splitoff
Incremental revenue
Less: Further processing costs
Additional contribution from further processing
3.
Units
6,000
600
5,400
Dollars
$540,000
360,000
180,000
110,000
$ 70,000
Assuming Sundown Sawmill, Inc., announces that in six months it will sell the rough-cut
product at splitoff due to increasing competitive pressure, behavior that may be
demonstrated by the skilled labor in the planing and sizing process include the following:
•
•
•
lower quality,
reduced motivation and morale, and
job insecurity, leading to nonproductive employee time looking for jobs elsewhere.
Management actions that could improve this behavior include the following:
•
•
•
Improve communication by giving the workers a more comprehensive explanation as
to the reason for the change so they can better understand the situation and bring out a
plan for future operation of the rest of the plant.
The company can offer incentive bonuses to maintain quality and production and
align rewards with goals.
The company could provide job relocation and internal job transfers.
16-32
SOLUTION EXHIBIT 16-29
Joint Costs
$1,200,000
Separable Costs
Studs
$8 per unit
Raw Decorative
Pieces
$60 per unit
Processing
Processing
$110,000
Posts
$20 per unit
Splitoff
Point
16-33
Decorative
Pieces
$100 per unit
16-30 (40 min.) Joint-cost allocation.
1.
Joint Costs
$20,000
Separable Costs
Butter
Processing
$.5 per pound
Spreadable
Butter
Milk
Processing
For P. 16-31
Buttermilk
Buttermilk
Processing
$.25 per pint
SPLITOFF
POINT
a.
Physical-measure method:
Physical measure of total production
(10,000 lbs × 2; 20,000 qts × 4)
Weighting, 20,000; 80,000 ÷ 100,000
Joint costs allocated,
0.20; 0.80 × $20,000
Butter
Buttermilk
Total
20,000 cups
80,000 cups
100,000 cups
0.20
0.80
$4,000
$16,000
$20,000
b. Sales value at splitoff method:
Sales value of total production at splitoff,
10,000 × $2; 20,000 × $1.5
Weighting, $20,000; $30,000 ÷ $50,000
Joint costs allocated,
0.40; 0.60 × $20,000
16-34
Butter
$20,000
Buttermilk
$30,000
0.40
0.60
$8,000
$12,000
Total
$50,000
$20,000
c.
Net realizable value method:
Butter
Final sales value of total production,
20,000 × $2.5; 20,000 × $1.5
Deduct separable costs
Net realizable value
Weighting, $45,000; $30,000 ÷ $75,000
Joint costs allocated,
0.60; 0.40 × $20,000
d.
Buttermilk
Total
$50,000
5,000
$45,000
0.60
$30,000
-0- .
$ 30,000
0.40
$80,000
5,000
$75,000
$12,000
$8,000
$20,000
Constant gross-margin percentage NRV method:
Step 1:
Final sales value of total production,
Deduct joint and separable costs, ($20,000 + $5,000)
Gross margin
Gross-margin percentage ($55,000 ÷ $80,000)
$80,000
25,000
$ 55,000
68.75%
Step 2:
Final sales value of total
production (see 1c.)
Deduct gross margin, using overall
gross-margin percentage of sales (68.75%)
Total production costs
Butter
Buttermilk
Total
$50,000
$30,000
$80,000
34,375
15,625
20,625
9,375
55,000
25,000
5,000
$10,625
-0- .
$ 9,375
5,000
$20,000
Step 3:
Deduct separable costs
Joint costs allocated
2.
Advantages and disadvantages:
- Physical-Measure
Advantage: Low information needs. Only knowledge of joint cost and physical
distribution is needed.
Disadvantage: Allocation is unrelated to the revenue-generating ability of products.
16-35
- Sales Value at Splitoff
Advantage: Considers market value of products as basis for allocating joint cost.
Relative sales value serves as a proxy for relative benefit received by each product from
the joint cost.
Disadvantage: Uses selling price at the time of splitoff even if product is not sold by the
firm in that form. Selling price may not exist for product at splitoff.
- Net Realizable Value
Advantages: Allocates joint costs using ultimate net value of each product; applicable
when the option to process further exists
Disadvantages: High information needs; Makes assumptions about expected outcomes of
future processing decisions
- Constant Gross-Margin percentage method
Advantage: Since it is necessary to produce all joint products, they all look equally
profitable.
Disadvantages: High information needs. All products are not necessarily equally
profitable; method may lead to negative cost allocations so that unprofitable products are
subsidized by profitable ones.
3.
When selling prices for all products exist at splitoff, the sales value at split off method is
the preferred technique. It is a relatively simple technique that depends on a common
basis for cost allocation – revenues. It is better than the physical method because it
considers the relative market values of the products generated by the joint cost when
seeking to allocate it (which is a surrogate for the benefits received by each product from
the joint cost). Further, the sales value at splitoff method has advantages over the NRV
method and the constant gross margin percentage method because it does not penalize
managers by charging more for developing profitable products using the output at
splitoff, and it requires no assumptions about future processing activities and selling
prices.
16-36
16-31 (10 min.) Further processing decision (continuation of 16-30).
1.and 2.
The decision about which combination of products to produce is not affected by the
method of joint cost allocation. For both the sales value at splitoff and physical measure
methods, the relevant comparisons are as shown below:
Sell at Splitoff – Revenue
Process Further - NRV
Profit (Loss) from Processing Further
Butter
$20,000 a
$45,000 c
$25,000
Buttermilk
$30,000 b
$32,000 d
$2,000
a
10,000 lbs × $2 = $20,000
20,000 qts × $1.5 = $30,000
c
20,000 tubs × $2.5 – 10,000lbs × $.5 = $45,000
d
40,000 pints × $1 – 40,000 pints × $.2 = $32,000
b
To maximize profits, Elsie should process butter further into spreadable butter. However,
Elsie should also sell the buttermilk in the pint containers. The extra cost to convert to
pint containers ($0.2 per pint × 2 pints per quart = $0.40 per quart) does not exceed the
increase in selling price ($1 per pint × 2 pints per quart = $2 per quart - $1.50 original
price = $0.50 per quart) and leads to a gain of $2,000.
3.
The decision to sell a product at split off or to process it further should have nothing to do
with the allocation method chosen. For each product, you need to compare the revenue
from selling the product at split off to the NRV from processing the product further.
Other things being equal, management should choose the higher alternative. The total
joint cost is the same regardless of the alternative chosen and is therefore irrelevant to the
decision.
16-37
16-32 (20 min.) Joint-cost allocation with a byproduct.
1.
Sales value at splitoff method: Byproduct recognized at time of production method
Joint cost to be charged to joint products = Joint Cost – NRV of Byproduct
= $10,000 – 1000 tons × 20% × 0.25 vats × $60
= $10,000 – 50 vats × $60
= $ 7,000
Sales value of coal at splitoff,
1,000 tons × .4 × $100; 1,000 tons × .4 × $60
Weighting, $40,000; $24,000 ÷ $64,000
Joint costs allocated,
0.625; 0.375 × $7,000
Gross Margin (Sales Revenue-Allocated Cost)
2.
Grade A
Coal
$40,000
Grade B
Coal
$24,000
Total
0.625
0.375
$4,375
$2,625
$ 7,000
$35,625
$21,375
$57,000
$64,000
Sales value at splitoff method: Byproduct recognized at time of sale method
Joint cost to be charged to joint products = Total Joint Cost = $10,000
Sales value of coal splitoff,
1,000 tons × .4 × $100; 1,000 tons × .4 × $60
Weighting, $40,000; $24,000 ÷ $64,000
Joint costs allocated,
0.625; 0.375 × $10,000
Gross Margin (Sales Revenue-Allocated Cost)
Grade A
Coal
$40,000
Grade B
Coal
$24,000
Total
0.625
0.375
$6,250
$3,750
$10,000
$33,750
$20,250
$54,000
$64,000
Since the entire production is sold during the period, the overall gross margin is the same
under the production and sales methods. In particular, under the sales method, the $3,000
received from the sale of the coal tar is added to the overall revenues, so that
Cumberland’s overall gross margin is $57,000, as in the production method.
3.
The production method of accounting for the byproduct is only appropriate if
Cumberland is positive they can sell the byproduct and positive of the selling price.
Moreover, Cumberland should view the byproduct’s contribution to the firm as material
enough to find it worthwhile to record and track any inventory that may arise. The sales
method is appropriate if either the disposition of the byproduct is unsure or the selling
price is unknown, or if the amounts involved are so negligible as to make it economically
infeasible for Cumberland to keep track of byproduct inventories.
16-38
16-33 (15 min.)
1.
Byproduct journal entries (continuation of 16-32).
Byproduct – production method journal entries
i) At time of production:
Work in process inventory
Accounts Payable, etc.
10,000
10,000
For byproduct:
Finished Goods Inv – Coal tar
Work in process inventory
3,000
For Joint Products
Finished Goods Inv – Grade A
Finished Goods Inv – Grade B
Work in process inventory
4,375
2,625
3,000
7,000
ii) At time of sale:
For byproduct
Cash or A/R
3,000
Finished Goods Inv – Coal Tar
3,000
For Joint Products
Cash or A/R
Sales Revenue – Grade A
Sales Revenue – Grade B
64,000
40,000
24,000
Cost of goods sold - Grade A
4,375
Cost of goods sold - Grade B
2,625
Finished Goods Inv – Grade A
4,375
Finished Goods Inv – Grade B
2,625
2.
Byproduct – sales method journal entries
i) At time of production:
Work in process inventory
Accounts Payable, etc.
10,000
10,000
For byproduct:
No entry
For Joint Products
Finished Goods Inv – Grade A
Finished Goods Inv – Grade B
Work in process inventory
16-39
6,250
3,750
10,000
ii) At time of sale
For byproduct
Cash or A/R
Sales Revenue – Coal Tar
For Joint Products
Cash or A/R
Sales Revenue – Grade A
Sales Revenue – Grade B
3,000
3,000
64,000
40,000
24,000
Cost of goods sold - Grade A
6,250
Cost of goods sold - Grade B
3,750
Finished Goods Inv – Grade A
6,250
Finished Goods Inv – Grade B
3,750
16-40
16-34 (40 min.) Process further or sell, byproduct.
1.
The analysis shown below indicates that it would be more profitable for Newcastle
Mining Company to continue to sell bulk raw coal without further processing. This
analysis ignores any value related to coal fines. It also assumes that the costs of loading
and shipping the bulk raw coal on river barges will be the same whether Newcastle sells
the bulk raw coal directly or processes it further.
Incremental sales revenues:
Sales revenue after further processing (9,400,000a tons × $36)
Sales revenue from bulk raw coal (10,000,000 tons × $27)
Incremental sales revenue
$338,400,000
270,000,000
68,400,000
Incremental costs:
Direct labor
Supervisory personnel
Heavy equipment costs ($25,000 × 12 months)
Sizing and cleaning (10,000,000 tons × $3.50)
Outbound rail freight (9,400,000 tons ÷ 60 tons) × $240 per car
Incremental costs
Incremental gain (loss)
800,000
200,000
300,000
35,000,000
37,600,000
73,900,000
$(5,500,000)
a
10,000,000 tons × (1– 0.06)
2.
The cost of producing the raw coal is irrelevant to the decision to process further or not.
As we see from requirement 1, the cost of producing raw coal does not enter any of the
calculations related to either the incremental revenues or the incremental costs of further
processing. The answer would the same as in requirement 1: do not process further.
3.
The analysis shown below indicates that the potential revenue from the coal fines
byproduct would result in additional revenue, ranging between $4,950,000 and
$9,900,000, depending on the market price of the fines.
Coal fines
=
=
=
75% of 6% of raw bulk tonnage
0.75 × (10,000,000 × .06)
450,000 tons
Potential incremental income from preparing and selling the coal fines:
Incremental income per ton
(Market price – Incremental costs)
Incremental income ($11; $22 × 450,000)
Minimum
$11 ($15 – $4)
Maximum
$22 ($24 – $2)
$4,950,000
$9,900,000
16-41
The incremental loss from sizing and cleaning the raw coal is $5,500,000, as calculated in
requirement 1. Analysis indicates that relative to selling bulk raw coal, the effect of
further processing and selling coal fines is only slightly negative at the minimum
incremental gain ($4,950,000 – $5,500,000 = – $550,000) and very beneficial at the
maximum incremental gain ($9,900,000 – $5,500,000 = $4,400,000). NMC will benefit
from further processing and selling the coal fines as long as its incremental income per
ton of coal fines is at least $12.22 ($5,500,000 ÷ 450,000 tons). Hence, further processing
is preferred.
Note that other than the financial implications, some factors that should be considered in
evaluating a sell-or-process-further decision include:
• Stability of the current customer market for raw coal and how it compares to the
market for sized and cleaned coal.
• Storage space needed for the coal fines until they are sold and the handling costs of
coal fines.
• Reliability of cost (e.g., rail freight rates) and revenue estimates, and the risk of
depending on these estimates.
• Timing of the revenue stream from coal fines and impact on the need for liquidity.
• Possible environmental problems, i.e., dumping of waste and smoke from
unprocessed coal.
16-42
16-35 (30 min.) Accounting for a byproduct.
Note: This solution is based off of the problem update listed on the errata sheet in the front
matter of this solution manual.
1.
Byproduct recognized at time of production:
Joint Cost = ($240 × 40) + $8,000 = $17,600
Joint cost charged to main product = Joint Cost – NRV of Byproduct
= $17,600 – (4 × 40 scarves × $20)
= $17,600 – (160 scarves × $20)
= $14,400
Inventoriable cost of main product = $14,400 / 720 = $20.00 per blouse
Inventoriable cost of byproduct = NRV = $20 per scarf
Gross Margin Calculation under Production Method
Revenues
Main product: Blouses (600 blouses × $72)
Byproduct: Scarves
Cost of goods sold
Main product: Blouses (600 blouses × $20.00)
$43,200
0
$43,200
_______
$12,000
Gross margin
Gross-margin percentage ($31,200 ÷ $43,200)
$31,200
72.22%
Inventoriable costs (end of period):
Main product: Blouses (120 blouses × $20.00) = $2,400
Byproduct: Scarves (30 scarves × $20) = $600
2.
Byproduct recognized at time of sale:
Joint cost to be charged to main product = Total Joint Cost = $17,600
Inventoriable cost of main product = $17,600 / 720 = $24.44 per blouse
Inventoriable cost of byproduct = $0
16-43
Gross Margin Calculation under Sales Method
Revenues
Main product: Blouses (600 blouses × $72)
Byproduct: Scarves (130 scarves × $20)
Cost of goods sold
Main product: Blouses (600 blouses × $24.44)
$43,200
2,600
$45,800
_______
$14,667
Gross margin
Gross-margin percentage ($31,133 ÷ $45,800)
$31,133
67.98%
Inventoriable costs (end of period):
Main product: Blouses (120 blouses × $24.44) = $2,933
Byproduct: Scarves (30 scarves × $0) = $0
3. (a) Byproduct – production method journal entries
i) At time of production:
Work in process inventory
Accounts payable, etc.
17,600
17,600
For byproduct:
Finished Goods Inv – Scarves
Work in process inventory
3,200
For main product
Finished Goods Inv – Blouses
Work in process inventory
14,400
3,200
14,400
ii) At time of sale:
For byproduct
Cash or A/R
2,600
Finished Goods Inv – Scarves
2,600
For main product
Cash or A/R
Sales Revenue – Blouses
43,200
43,200
Cost of goods sold - Blouses
12,000
Finished Goods Inv – Blouses
12,000
16-44
(b) Byproduct – sales method journal entries
i) At time of production:
Work in process inventory
Accounts payable, etc.
17,600
17,600
For byproduct:
No entry
For Joint Product
Finished Goods Inv – Blouses
Work in process inventory
ii) At time of sale:
For byproduct
Cash or A/R
Sales Revenue – Scarves
For Joint Product
Cash or A/R
Sales Revenue – Blouses
17,600
17,600
2,600
2,600
43,200
43,200
Cost of goods sold - Blouses
14,667
Finished Goods Inv – Blouses
14,667
16-45
Collaborative Learning Problem
16-36 (60 min.) Joint Cost Allocation
1.
(a) The Net Realizable Value Method allocates joint costs on the basis of the relative
net realizable value (final sales value minus the separable costs of production and
marketing). Joint costs would be allocated as follows:
Final sales value of total production
Deduct separable costs
Net realizable value at splitoff point
Weighting ($23,500; $7,500 ÷ $31,000)
Joint costs allocated (0.7581; 0.2419 × $24,000)
Total production costs
($18,194 + $1,500; $5,806 + $1,000)
Production costs per unit
($19,694; $6,806 ÷ 500 units)
(b)
Deluxe
Module
$25,000
1,500
$23,500
0.7581
$18,194
Standard
Module
$ 8,500
1,000
$ 7,500
0.2419
$ 5,806
$19,694
$ 6,806
$ 39.39
$ 13.61
Total
$33,500
2,500
$31,000
$24,000
$26,500
The constant gross-margin percentage NRV method allocates joint costs in such a way
that the overall gross-margin percentage is identical for all individual products as follows:
Step 1
Final sales value of total production:
(Deluxe, $25,000; Standard, $8,500)
Deduct joint and separable costs (Joint, $24,000 +
Separable Deluxe, $1,500 + Separable Standard, $1,000)
Gross margin
Gross-margin percentage ($7,000 ÷ $33,500)
$33,500
26,500
$ 7,000
20.8955%
Step 2
Final sales value of total production
Deduct gross margin using overall gross
margin percentage (20.8955%)
Total production costs
Deluxe
Module
$25,000
Standard
Module
$8,500
Total
$33,500
5,224
19,776
1,776
6,724
7,000
26,500
1,500
$18,276
1,000
$5,724
2,500
$24,000
$ 39.55
$13.45
Step 3
Deduct separable costs
Joint costs allocated
Production costs per unit ($19,776;
$6,724 ÷ 500 units)
16-46
(c)
The physical measure method allocates joint costs on the basis of the relative
proportions of total production at the splitoff point, using a common physical measure
such as the number of bits produced for each type of module. Allocation on the basis of
the number of bits produced for each type of module follows:
Physical measure of total production (bits)
Weighting (500,000; 250,000 ÷ 750,000)
Joint costs allocated (0.6667; 0.3333 × $24,000)
Total production costs
($16,000 + $1,500; $8,000 + $1,000)
Production costs per unit
($17,500; $9,000 ÷ 500 units)
Deluxe
Module/
Chips
Standard
Module/
Chips
500,000
0.6667
$16,000
250,000
0.3333
$ 8,000
$24,000
$17,500
$ 9,000
$26,500
$ 35.00
$18.00
Total
750,000
Each of the methods for allocating joint costs has weaknesses. Because the costs are joint
in nature, managers cannot use the cause-and-effect criterion in making this choice.
Managers cannot be sure what causes the joint costs attributable to individual products.
The net realizable value (NRV) method (or sales value at splitoff method) is widely used when
selling price data are available. The NRV method provides a meaningful common denominator
to compute the weighting factors. It allocates costs on the ability-to-pay principle. It is probably
preferred to the constant gross-margin percentage method which also uses sales values to
allocate costs to products. That’s because the constant gross-margin percentage method makes
the further tenuous assumption that all products have the same ratio of cost to sales value.
The physical measure method bears little relationship to the revenue-producing power of the
individual products. Several physical measures could be used such as the number of chips and
the number of good bits. In each case, the physical measure only relates to one aspect of the
chip that contributes to its value. The value of the module as determined by the marketplace is a
function of multiple physical features. Another key question is whether the physical measure
chosen portrays the amount of joint resources used by each product. It is possible that the
resources required by each type of module depend on the number of good bits produced during
chip manufacturing. But this cause-and-effect relationship is hard to establish.
MMC should use the NRV method. But the choice of method should have no effect on
their current control and measurement systems.
16-47
2.
The correct approach in deciding whether to process further and make DRAM modules from
the standard modules is to compare the incremental revenue with the incremental costs:
Incremental revenue from making DRAMs ($26 × 400) – ($17 × 500)
Incremental costs of DRAMs, further processing
Incremental operating income from converting standard modules
into DRAMs
$1,900
1,600
$ 300
A total income computation of each alternative follows:
Alternative 1:
Sell Deluxe
and Standard
Total revenues ($25,000 + $8,500) $33,500
Total costs
26,500
Operating income
$ 7,000
Alternative 2:
Sell Deluxe
and DRAM
Difference
($25,000 + $10,400) $35,400
($26,500 + $1,600) 28,100
$ 7,300
$1,900
1,600
$ 300
It is profitable to extend processing and to incur additional costs on the standard module
to convert it into a DRAM module as long as the incremental revenue exceeds incremental costs.
The amount of joint costs incurred up to splitoff ($24,000)––and how these joint costs are
allocated to each of the products––are irrelevant to the decision of whether to process further and
make DRAMS. That’s because the joint costs of $24,000 remain the same whether or not further
processing is done on the standard modules.
Joint-cost allocations using the physical measure method (on the basis of the number of
bits) may mislead MMC, if MMC uses unit-cost data to guide the choice between selling
standard modules versus selling DRAM modules. In requirement 2, allocating joint costs on the
basis of the number of good bits yielded a cost of $16,000 for the Deluxe modules and $8,000 for
the Standard modules. A product-line income statement for the alternatives of selling Deluxe
modules and DRAM modules would appear as follows:
Deluxe Module
Revenues
Cost of goods sold
Joint costs allocated
Separable costs
Total cost of goods sold
Gross margin
DRAM Module
$25,000
$10,400
16,000
1,500
17,500
$ 7,500
8,000
2,600*
10,600
$ (200)
*Separable costs of $1,000 to manufacture the Standard module and further separable costs of
$1,600 to manufacture the DRAM module.
16-48
This product-line income statement would erroneously imply that MMC would suffer a
loss by selling DRAMs, and as a result, it would suggest that MMC should not process further to
make and sell DRAMs. This occurs because of the way the joint costs are allocated to the two
products. As mentioned earlier, the joint-cost allocation is irrelevant to the decision. On the basis
of the incremental revenues and incremental costs, MMC should process the Standard modules
into DRAM modules.
16-49